nth derivative of (x+1)n is equal to
(n-1)!
(n+1)!
n!
n[(n+1)]n-1
Explanation for the correct option:
Finding the nth derivative:
Let
y=(x+1)ndydx=n(x+1)n-1d2yd2x=n(n-1)(x+1)n-2d3yd3x=n(n-1)(n-2)(x+1)n-3
Similarly nth derivative,
dnydnx=n(n-1)(n-2)…(n-(n-1))(x+1)n-n
=n(n-1)(n-2)…(1)(x+1)0
=n!
Therefore, the nth derivative of (x+1)n =n!
Hence, option(C) is the correct answer.